Subgroups — #49097586

Order 35968.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823865	C₂	1	1	yes	maximal, characteristic
2	#31823290	C₂	1	2	yes	maximal
3	#31823288	C₂	1	2	yes	maximal
4	#31823239	C₂	1	1	yes	maximal, characteristic
5	#500×C₂₈₁	C₂	1	1	yes	maximal, characteristic
6	#22582871	—	2	1	no	—
7	C₂×#17985113	C₂²	1	2	yes	—
8	#22582813	C₂²	1	1	yes	characteristic
9	#22582813	C₂²	1	1	yes	characteristic
10	#22582811	—	2	1	no	—
11	C₄⋊Q₈×C₂₈₁	—	2	1	no	—
12	#107×C₂₈₁	—	2	1	no	—
13	#107×C₂₈₁	C₂²	1	2	yes	—
14	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₂₈₁	—	2	1	no	—
16	C₄⋊Dic₂₈₁	—	2	1	no	—
17	#17985117	—	4	1	no	—
18	#17985117	—	4	1	no	—
19	#17985113	Q₈	1	4	yes	complemented
20	C₂×Q₈×C₂₈₁	—	4	1	no	—
21	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₂₈₁	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₂₈₁	—	2	2	no	—
24	C₄⋊C₄×C₂₈₁	—	4	1	no	—
25	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
26	C₂×Dic₂₈₁	—	4	1	no	—
27	C₂×Dic₂₈₁	—	4	1	no	—
28	Q₈×C₂₈₁	—	8	2	no	—
29	C₂×C₄×C₂₈₁	—	4	2	no	—
30	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
31	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
32	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
33	C₈×C₂₈₁	Q₁₆	1	2	yes	—
34	C₈×C₂₈₁	C₂×Q₈	1	2	yes	—
35	C₂²×C₂₈₁	C₂×D₈	1	1	yes	characteristic
36	C₄×C₂₈₁	—	2	1	no	—
37	C₄×C₂₈₁	—	2	1	no	—
38	C₄×C₂₈₁	—	8	2	no	—
39	C₄×C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic
40	C₄×C₂₈₁	C₂×Q₁₆	1	1	yes	characteristic
41	Dic₂₈₁	—	8	1	no	—
42	Dic₂₈₁	—	8	1	no	—
43	C₂×C₂₈₁	#500	1	1	yes	characteristic
44	C₂×C₂₈₁	#509	1	1	yes	characteristic
45	C₂×C₂₈₁	#510	1	1	yes	characteristic
46	C₂₈₁	#2255	1	1	yes	characteristic, complemented, Sylow
47	#2255	—	281	1	no	maximal, Sylow
48	#500	D₂₈₁	1	1	yes	characteristic
49	#499	—	281	1	no	—
50	#367	—	281	2	no	—
51	#366	—	281	2	no	—
52	#346	—	281	1	no	—
53	C₄⋊Q₈	—	2	1	no	—
54	#125	—	562	1	no	—
55	C₂×C₁₆	—	281	2	no	—
56	#107	—	2	1	no	—
57	#107	—	281	1	no	—
58	#107	—	281	1	no	—
59	#107	C₂×D₂₈₁	1	2	yes	—
60	#106	—	562	1	no	—
61	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
62	C₂×Q₈	—	4	1	no	—
63	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₂₈₁	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	562	1	no	—
68	C₄⋊C₄	—	562	1	no	—
69	C₄⋊C₄	—	1124	1	no	—
70	C₄⋊C₄	—	1124	1	no	—
71	C₄²	C₂²⋊D₂₈₁	1	1	yes	characteristic
72	C₁₆	—	281	4	no	—
73	Q₈	—	8	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	1124	1	no	—
76	C₂×C₄	—	1124	1	no	—
77	C₂×C₄	#17985123	1	1	yes	characteristic
78	C₂×C₄	#17985123	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
80	C₈	#17985128	1	2	yes	—
81	C₈	Q₈×D₂₈₁	1	2	yes	—
82	C₂²	C₂×#17985123	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	2	no	—
86	C₄	—	2248	1	no	—
87	C₄	—	2248	1	no	—
88	C₄	#22582877	1	1	yes	characteristic
89	C₄	C₂×#17985128	1	1	yes	characteristic
90	C₂	#31823866	1	1	yes	characteristic
91	C₂	#31823899	1	1	yes	characteristic
92	C₂	#31823904	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#17985123
commutator, cosocle	C₂×C₈×C₂₈₁	C₂³
Frattini	C₂×C₈	C₂²×D₂₈₁
Fitting	#500×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₂×D₈
hypercenter	#500	D₂₈₁
hypocenter	C₂₈₁	#2255
LCS	G ▷ C₂×C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
19. #17985113	Q₈	semidirect
46. C₂₈₁	#2255	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#31823865	2
#31823290	2
#31823288	2
#31823239	2
#500×C₂₈₁	2
#2255	281